Does SONY have the exclusive rights to any computer game about the WRC
Rally? Does that include any kind of internet game developed as part
of an advertising promotion?

Yes and No.

Sony have rights to the WRC rally through a company called Evolution
Studios based in Liverpool UK. Sony have very strong ties with this
company but do not own them outright.
Currently, the next Generation version of a WRC game is *probably*
under development by Evoultion studios and will *probably* feature
online play.

However - what Sony do not own is complete rights to any Rally game.
There are several other competitors on the market such as Codemasters
Popular Colin McCrae license.

It would be unwise to make a rally game claiming to be an officially
sponsored WRC game as that license is owned by Sony/Evolution. That
would be a basis for license infringement and you would be likely be
sued. However a more generic "rally game" could easily be made with no
legal repercussions. (Otherwise similar games of any type would not be
possible)